Hydrodynamic Lubrication Pdf

[Toney Talbot]

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Boundary lubrication is associated with metal-to-metal contact between two sliding surfaces of the machine. During initial start-up or shutdown of some equipment (e.g., journal bearings) or under heavily loaded conditions (pins and bushings of construction equipment), the metal surfaces in a lubricated system may actually come into severe contact with each other. If the oil film is not thick enough to overcome the surface roughness of the metal, a lambda value of less than one results.

We generally want to avoid boundary lubrication where possible. It is agreed among lubrication specialists that friction may be at its highest level during the boundary lubrication regime. This occurs at start-up, shutdown, low speed or high load conditions.

Boundary lubrication regimes occur during any condition where the asperities of two lubricated surfaces in relative motion may come into physical contact and the potential for abrasion and/or adhesion occurs. It has been suggested by lubrication engineers and tribologists that as much as 70 percent of wear occurs during the start-up and shutdown phases of machinery.

A back-up or secondary method of reducing this phenomenon of the boundary lubrication regime is with the use of a fully formulated lubricant that includes anti-wear or extreme pressure additives. These additives react with the metal asperities that have come into contact by responding to the high pressure and high temperature of contact and instantly forming an altered ductile (pliable) film on the metal (iron) surface.

Generally speaking, boundary lubrication is dramatically reduced as sliding speed increases, creating a wedge of lubricant film between the surfaces in motion. As the potential for asperity contact is reduced and film thickness is increased, the coefficient of friction drops dramatically to the condition known as mixed lubrication.

Some metal-to-metal asperity loading is still occurring combined with loading (lift) on the lubricant. This is an intermediary condition between boundary and hydrodynamic/elastohydrodynamic lubrication regimes, the gray area between them. As the oil film thickness increases further, the system now moves into full film lubrication, either elastohydrodynamic or hydrodynamic lubrication.

This lubrication regime occurs between sliding surfaces when a full film of oil supports and creates a working clearance (e.g., between a rotating shaft and journal bearing). In order for hydrodynamic lubrication to be successfully and completely applied, there must be a high degree of geometric conformity between the machine components (e.g., the curve of the shaft and the curve of the shell in a journal bearing are very similar) and a resulting low-contact pressure (100 to 300 psi in industrial journal bearings) between the surfaces in relative motion.

This lubrication regime condition occurs after a machine has begun to rotate and the speeds and loads are such that a wedge of oil has been formed between the shaft and bearing surfaces. This wedge of oil lifts the shaft away from the bearing surface so there is little risk of asperity contact. This is a desirable condition to avoid friction and wear.

Any friction remaining is found within the lubricant itself, as the molecular structures of the oil slide past each other during operation. Oil films are typically in the order of 2 to 100 microns (0.00008 to 0.004 inches) thick. They can be larger (300 microns or 0.012 inches) in very large diameter journal bearings. Lambda values (oil film thickness to surface roughness ratio) are usually greater than 2.

Elastohydrodynamic lubrication conditions occur when a rolling motion exists between the moving elements, and the contact zone has a low degree of conformity. For example, note that the curve of the roller and the race in a rolling element bearing are very dissimilar.

In fact, the roller and inner race are curved in opposite directions and thus have a small contact area (almost a single point of contact). This creates high-contact pressures (hundreds of thousands of psi).

Examples of machinery applications that operate under EHL are rolling element bearings, gear teeth and cam contacts (rolling) where high rolling contact loads occur. If operating conditions such as speeds, loads and temperatures are not exceeded, asperity contact may never occur due to this remarkable characteristic of lubricant and metal.

The oil film thicknesses are often in the order of 1 micron (very, very thin). However, EHL is considered to operate on a full fluid (oil) film (surface asperity heights are in the order of 0.4 to 0.8 microns).

We study how hydrodynamic interactions affect the collective behaviour of active particles suspended in a fluid at high concentrations, with particular attention to lubrication forces which appear when the particles are very close to one another. We compute exactly the limiting behaviour of the hydrodynamic interactions between two spherical (circular) active swimmers in very close proximity to one another in the general setting in both three and (two) dimensions. Combining this with far-field interactions, we develop a novel numerical scheme which allows us to study the collective behaviour of large numbers of active particles with accurate hydrodynamic interactions when close to one another. We study active swimmers whose intrinsic flow fields are characterised by force dipoles and quadrupoles. Using this scheme, we are able to show that lubrication forces when the particles are very close to each other can play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that when the swimmer force dipole is large, finite clusters and open gel-like clusters appear rather than complete phase separation. This suppression is due to near-field lubrication interactions. For swimmers with small force dipoles, we find surprisingly that a globally polar-ordered phase appears because near-field lubrication rather than long-range hydrodynamics dominates the alignment mechanism. Polar order is present for very large system sizes and is stable to fluctuations with a finite noise amplitude. We explain the emergence of polar order using a minimal model in which only the leading rotational effect of the near-field interaction is included. These phenomena are also reproduced in two dimensions.

Although the fundamental equation for hydrodynamic lubrication was derived by Reynolds [1] almost 140 years ago, accurate descriptions of thin-film fluid flow are still a research topic of ongoing interest. Major challenges in modeling arise in elastohydrodynamic lubrication (EHL), where a plethora of effects, such as non-Newtonian fluid behavior, surface roughness, wall slip, or cavitation, has to be considered. An extensive overview of the field of EHL is given in the review articles by Lugt and Morales-Espejel [2] and Gropper et al. [3], the latter focusing on textured surfaces.

However, fluid compressibility and pressure-dependent viscosity cannot be ignored under severe loading conditions, such as in EHL contacts. It is therefore common practice to introduce constitutive relations for the pressure-dependent density and viscosity to the asymptotic analysis a posteriori. Yet, this can lead to wrong predictions for piezoviscous fluids, where the viscosity strongly depends on pressure [5,6,7].

In this paper, we present a novel method that requires no a priori assumptions on the form of the constitutive equations. Our splitting approach for the conserved variables in the three-dimensional mass and momentum balance leads to two separate problems: a macro problem, which describes the time evolution of height-averaged variables in two spatial dimensions, and a micro problem, which determines the local stress state given the macroscopic flow and boundary conditions. The solution procedure for the macro problem is therefore independent of the type of constitutive equation used in the micro problem.

We demonstrate the validity of our method by solving the micro problem for Newtonian and generalized Newtonian fluids and compare the results from our transient finite-volume implementation with various Reynolds-based solutions from the literature. Moreover, the formulation in terms of conserved variables allows a flexible implementation of cavitation models through the equation of state. We also demonstrate Navier slip boundary conditions for the investigation of lubrication with heterogeneous surface wettability.

Hence, the averaged scheme is composed of a two-dimensional divergence operator acting on height-averaged flux functions and of terms containing both averaged and unaveraged flux functions, the latter evaluated at the top and bottom walls. The terms outside of the divergence operator can be regarded as geometrical source terms due to the reduction of dimensionality.

We use the simplified source term for the numerical tests presented in Sect. 4, but more complicated boundary conditions are generally possible. Hence, for flat channels, where the gradients of the lower wall disappear, the source term only consists of momentum flux contributions in z-direction evaluated at the upper and lower wall, respectively.

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